After complete graphs, the next most natural question to consider regarding weak saturation numbers is description of the behavior of \(\mathrm {wsat}(n, K_{s,t})\) , where \(K_{s,t}\)  is the complete bipartite graph with parts of sizes \(s\)  and \( t \) . Borowiecki and Sidorowicz [1]} proved that \(\mathrm {wsat}(n, K_{1,t})=\binom{t}{2}\)  provided \(n\geqslant t+1\) . A short proof of this result is given in [2]}.
The equality \(\mathrm {wsat}(n, K_{2,2})=n\)  follows from Theorem 16 of [1]} for all \(n\geqslant 4\) .
Faudree, Gould, and Jacobson [2]} showed that \(\mathrm {wsat}(n, K_{2,3})=n+1\)  for all \(n\geqslant 5\) .
Kalai [5]} established that \(\mathrm {wsat}(n, K_{t, t})=(t-1)n-\binom{t-1}{2}\)  if \(n\geqslant 4t-4\) .
This result is also proved by Kronenberg, Martins, and Morrison [6]} for \(n\geqslant 3t-3\)  by a linear algebraic argument.
They posed the following question: For every two positive integers \(s, t \)  with \(t>s\) ,
is there an integer \(n_0\)  such that \(\mathrm {wsat}(n, K_{s,t})=(s-1)(n-s)+\binom{t}{2}\)  for any integer \(n\geqslant n_0\) ?
They affirmatively answered to the question for \(t=s+1\) .
